**Quotients of Lie Groups**

If *G* is a Lie group and *N* is a normal Lie subgroup of *G*, the quotient *G* / *N* is also a Lie group. In this case, the original group *G* has the structure of a fiber bundle (specifically, a principal *N*-bundle), with base space *G* / *N* and fiber *N*.

For a non-normal Lie subgroup *N*, the space *G* / *N* of left cosets is not a group, but simply a differentiable manifold on which *G* acts. The result is known as a homogeneous space.

Read more about this topic: Quotient Group

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